Assuming that “integer” means 32 bits: 10 MB of space is more than enough for you to count how many numbers there are in the input file with any given 16-bit prefix, for all possible 16-bit prefixes in one pass through the input file. At least one of the buckets will have be hit less than 216 times. Do a second pass to find of which of the possible numbers in that bucket are used already.
If it means more than 32 bits, but still of bounded size: Do as above, ignoring all input numbers that happen to fall outside the (signed or unsigned; your choice) 32-bit range.
If “integer” means mathematical integer: Read through the input once and keep track of the largest number length of the longest number you’ve ever seen. When you’re done, output the maximum plus one a random number that has one more digit. (One of the numbers in the file may be a bignum that takes more than 10 MB to represent exactly, but if the input is a file, then you can at least represent the length of anything that fits in it).